Question

1. a builder is remodeling a kitchen. she creates the following scale drawing, which represents a countertop. the sink will not be covered with countertop. all actual lengths of the countertop are measured in feet. how many square feet of countertop area are needed?

Explanation:

Step1: Calculate semicircle area

The diameter is 3 ft, so radius $r=\frac{3}{2}$ ft. Area of semicircle: $\frac{1}{2} \pi r^2 = \frac{1}{2} \pi (\frac{3}{2})^2 = \frac{9\pi}{8} \approx 3.53$ sq ft

Step2: Calculate top rectangle area

Dimensions 4 ft × 3 ft. Area: $4 \times 3 = 12$ sq ft

Step3: Calculate right vertical rectangle area

Dimensions 5 ft × 4 ft. Area: $5 \times 4 = 20$ sq ft

Step4: Calculate sink (square) area

Dimensions 2 ft × 2 ft. Area: $2 \times 2 = 4$ sq ft

Step5: Calculate middle lower rectangle area

Dimensions 3 ft × 4 ft. Area: $3 \times 4 = 12$ sq ft

Step6: Calculate bottom left square area

Dimensions 3 ft × 3 ft. Area: $3 \times 3 = 9$ sq ft

Step7: Calculate bottom right rectangle area

Dimensions 5 ft × 3 ft. Area: $5 \times 3 = 15$ sq ft

Step8: Sum all areas minus sink

Total area = $3.53 + 12 + 20 + 12 + 9 + 15 - 4$

Answer:

$67.53$ square feet (or $\frac{9\pi}{8}+64 \approx 67.53$ square feet)